Question

If 4 tan θ = 3,evaluate (4 sin θ- cos θ + 1)/(4 sin θ + cos θ -1)

Answer 1

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THE ANSWER IS HERE,

Let the theta be a for my convenience .

=> 4tana = 3.

=> Tan a=3/4.

We know that,

Tan a= opp side /adj side.

$= > \: hypotenuse \: = \sqrt{ {opp \: side}^{2} + {adj \: side \: }^{2} }$

$= > \: \sqrt{ {3}^{2} + {4}^{2} }$
$= > \: \sqrt{25}$

$= > \: 5$

So,

Sina = opp side/hypotenuse.

=> 3/5.

Cos a= adj side/ hypotenuse.

=> 4/5.

From the question,

$= > \: \frac{4 \sin(a) - \cos(a) + 1 }{4 \sin(a) + \cos(a) - 1}$

$= > \: \frac{4( \frac{3}{5} ) - \frac{4}{5} + 1 }{4( \frac{3}{5}) + \frac{4}{5} - 1 }$


$= > \: \frac{ \frac{12 - 4 + 5}{5} }{ \frac{12 + 4 - 5}{5} }$

$= > \: \frac{13}{11}$

:-)Hope it helps u.